I have told all my friends and (close) family. In some cases, just because I felt like sharing what happened to me. In these cases, to me it is just a part of friendship that you share intimate, difficult experiences. Friends tell me stuff they are troubled by, I do the same. To me it is not even primarily about getting support in such cases, although I will get it and appreciate it. But it just seems to me it is what friendship consists of, sharing your difficult moments, embarrassing moments etc. I take comfort in my friends knowing who I am, as I do in knowing who they are.
That being said I do not have experience with this illness in a full-time work-environment, I’m still studying at university. Now I have disclosed my illness there as well, to some fellow students that I consider friends, as well as to some supervisors of mine. These latter may come closest to co-workers in terms of what kind of relationship and what level of trust there is between you. There are some differences as well. These teachers I have disclosed to are very educated in general, and also on the topic of schizophrenia and mental illness in general. They know about the symptoms, and they also knew my academic performance for a few years already before I disclosed. They were very understanding and I am glad to have told them. In general, so far I have not regretted telling anyone about my illness, and have not experienced stigma - though it is always possible people speak differently behind my back of course, worrying about this to me resembles paranoia too much to be attractive to me.
In general I have disclosed many times when the conversation naturally lead to a question to which the honest answer would involve disclosing my illness. But as said, this for me has been always in the context of relations of quite a high level of trust.
When the relationship is more superficial, and conversation presses for an explanation like you describe, I think some vagueness is allowed. You could say something like ‘I needed a break from it all’ and the co-workers you are least familiar with, I think, are also least likely to press the issue any further. In your situation, I would disclose only to co-workers I have established a personal relationship with. Like coming over for dinner, and disclosing other, less severe, personal matters. It is my experience that in the process of getting to know someone better and better, people will almost naturally disclose more and more personal matters. It is a sort of give and take. I can give the example of a fellow student that was becoming a friend and disclosed to me some issues he had with his girlfriend. I took that as my cue that it would be okay to disclose my mental illness to him. After that, he turned out to become one of my best friends.